## Class FastCosineTransform

• All Implemented Interfaces:
Function<double[],​double[]>, UnaryOperator<double[]>, RealTransform

public class FastCosineTransform
extends Object
implements RealTransform
Implements the Fast Cosine Transform for transformation of one-dimensional real data sets. For reference, see James S. Walker, Fast Fourier Transforms, chapter 3 (ISBN 0849371635).

There are several variants of the discrete cosine transform. The present implementation corresponds to DCT-I, with various normalization conventions, which are specified by the parameter FastCosineTransform.Norm.

DCT-I is equivalent to DFT of an even extension of the data series. More precisely, if x0, …, xN-1 is the data set to be cosine transformed, the extended data set x0#, …, x2N-3# is defined as follows

• xk# = xk if 0 ≤ k < N,
• xk# = x2N-2-k if N ≤ k < 2N - 2.

Then, the standard DCT-I y0, …, yN-1 of the real data set x0, …, xN-1 is equal to half of the N first elements of the DFT of the extended data set x0#, …, x2N-3#
yn = (1 / 2) ∑k=02N-3 xk# exp[-2πi nk / (2N - 2)]     k = 0, …, N-1.

The present implementation of the discrete cosine transform as a fast cosine transform requires the length of the data set to be a power of two plus one (N = 2n + 1). Besides, it implicitly assumes that the sampled function is even.

• ### Nested Class Summary

Nested Classes
Modifier and Type Class Description
static class  FastCosineTransform.Norm
Normalization types.
• ### Constructor Summary

Constructors
Constructor Description
FastCosineTransform​(FastCosineTransform.Norm normalization)
FastCosineTransform​(FastCosineTransform.Norm normalization, boolean inverse)
• ### Method Summary

All Methods
Modifier and Type Method Description
double[] apply​(double[] f)
Returns the transform of the specified data set.
double[] apply​(DoubleUnaryOperator f, double min, double max, int n)
Returns the transform of the specified function.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Methods inherited from interface java.util.function.Function

andThen, compose
• ### Constructor Detail

• #### FastCosineTransform

public FastCosineTransform​(FastCosineTransform.Norm normalization,
boolean inverse)
Parameters:
normalization - Normalization to be applied to the transformed data.
inverse - Whether to perform the inverse transform.
• #### FastCosineTransform

public FastCosineTransform​(FastCosineTransform.Norm normalization)
Parameters:
normalization - Normalization to be applied to the transformed data.
• ### Method Detail

• #### apply

public double[] apply​(double[] f)
Returns the transform of the specified data set.
Specified by:
apply in interface Function<double[],​double[]>
Specified by:
apply in interface RealTransform
Parameters:
f - the data array to be transformed (signal).
Returns:
the transformed array (spectrum).
Throws:
IllegalArgumentException - if the length of the data array is not a power of two plus one.
• #### apply

public double[] apply​(DoubleUnaryOperator f,
double min,
double max,
int n)
Returns the transform of the specified function.
Specified by:
apply in interface RealTransform
Parameters:
f - Function to be sampled and transformed.
min - Lower bound (inclusive) of the interval.
max - Upper bound (exclusive) of the interval.
n - Number of sample points.
Returns:
the result.
Throws:
IllegalArgumentException - if the number of sample points is not a power of two plus one, if the lower bound is greater than or equal to the upper bound, if the number of sample points is negative.